Mister Exam
Other calculators
- Derivative of a implicit defined function
- Derivative of Parametric Function
- Partial derivative of the function
- Curve tracing functions Step by Step
- Integral Step by Step
- Differential equations Step by Step
- Limits Step by Step
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How to use it?
- Derivative of:
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Derivative of x^(4/5)
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Derivative of 5*x^2-2/sqrt(x)+sin(pi/4)
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Derivative of x^3+2
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Derivative of x^2-7*x
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Identical expressions
- y=sqrt(arctg(x/ three))
- y equally square root of (arctg(x divide by 3))
- y equally square root of (arctg(x divide by three))
- y=√(arctg(x/3))
- y=sqrtarctgx/3
- y=sqrt(arctg(x divide by 3))
Derivative of y=sqrt(arctg(x/3))
The solution
You have entered
[src]
_________ / /x\ / atan|-| \/ \3/
$$\sqrt{\operatorname{atan}{\left(\frac{x}{3} \right)}}$$
sqrt(atan(x/3))
The first derivative
[src]
1 ------------------------ / 2\ _________ | x | / /x\ 6*|1 + --|* / atan|-| \ 9 / \/ \3/
$$\frac{1}{6 \left(\frac{x^{2}}{9} + 1\right) \sqrt{\operatorname{atan}{\left(\frac{x}{3} \right)}}}$$
The second derivative
[src]
/ 3 \
-3*|------- + 4*x|
| /x\ |
|atan|-| |
\ \3/ /
-------------------------
2 _________
/ 2\ / /x\
4*\9 + x / * / atan|-|
\/ \3/
$$- \frac{3 \left(4 x + \frac{3}{\operatorname{atan}{\left(\frac{x}{3} \right)}}\right)}{4 \left(x^{2} + 9\right)^{2} \sqrt{\operatorname{atan}{\left(\frac{x}{3} \right)}}}$$
The third derivative
[src]
/ 2 \
| 27 32*x 36*x |
3*|-8 + ----------------- + ------ + ----------------|
| / 2\ 2/x\ 2 / 2\ /x\|
| \9 + x /*atan |-| 9 + x \9 + x /*atan|-||
\ \3/ \3//
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2 _________
/ 2\ / /x\
8*\9 + x / * / atan|-|
\/ \3/
$$\frac{3 \left(\frac{32 x^{2}}{x^{2} + 9} + \frac{36 x}{\left(x^{2} + 9\right) \operatorname{atan}{\left(\frac{x}{3} \right)}} - 8 + \frac{27}{\left(x^{2} + 9\right) \operatorname{atan}^{2}{\left(\frac{x}{3} \right)}}\right)}{8 \left(x^{2} + 9\right)^{2} \sqrt{\operatorname{atan}{\left(\frac{x}{3} \right)}}}$$
The graph